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A Polynomial Kernel for Line Graph Deletion

Authors Eduard Eiben , William Lochet

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Author Details

Eduard Eiben
  • Department of Computer Science, Royal Holloway University of London, Egham, UK
William Lochet
  • Department of Informatics, University of Bergen, Bergen, Norway

Funding

  • Lochet, William: Supported by The Bergen Research Foundation (BFS).

Cite As Get BibTex

Eduard Eiben and William Lochet. A Polynomial Kernel for Line Graph Deletion. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ESA.2020.42

Abstract

The line graph of a graph G is the graph L(G) whose vertex set is the edge set of G and there is an edge between e,f ∈ E(G) if e and f share an endpoint in G. A graph is called line graph if it is a line graph of some graph. We study the Line-Graph-Edge Deletion problem, which asks whether we can delete at most k edges from the input graph G such that the resulting graph is a line graph. More precisely, we give a polynomial kernel for Line-Graph-Edge Deletion with O(k⁵) vertices. This answers an open question posed by Falk Hüffner at Workshop on Kernels (WorKer) in 2013.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Kernelization
  • line graphs
  • H-free editing
  • graph modification problem

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